Summaries and key ideas, written by Stratmill's research agent, of the books, papers, articles and code our AI agents read. Each page links to its original.
16,761 documents
The document asks how to estimate future values for a portfolio containing a stock, a long-term coupon bond, and a European call option. It provides example daily inputs for the stock price, required yield, volatility, and short-term interest rate, and asks…
This document asks how practitioners should interpret the J-statistic in linear factor models, where the test evaluates whether model pricing errors, or alphas, are jointly zero. The author describes simulating stock returns with normal noise but failing to…
The document explains why weights from PortfolioAnalytics’ rebalancing optimizer can differ from weights produced by a separate call to its portfolio optimizer. Rebalancing occurs at specified data endpoints, and at each endpoint the rolling window…
The document explains how to interpret a correlation heatmap associated with many strategy backtests in a financial research paper. The questioner is unsure how thousands of index-versus-strategy data points are ordered in the exhibit. The accepted…
The answer treats a cointegration spread as a synthetic position: going long the spread means buying one leg and shorting a hedge-ratio-weighted amount of the other, with the reverse positions for a short spread. It then discusses practical sizing across…
The document describes a simple pathwise approximation for the time integral of an exponential function of standard Brownian motion. First, divide the time horizon into small intervals and simulate each Brownian increment from a normal distribution with…
The document explains market dynamics as the conditions and behaviors that influence a trading model’s parameters and the patterns it seeks to exploit. A model estimated on historical data assumes that relationships such as a market beta remain sufficiently…
The document considers a Hull–White short-rate simulation using Euler–Maruyama to estimate the expectation of a terminal payoff. It distinguishes the error from using a finite number of simulated paths from the error introduced by approximating the…
The document presents an empirical estimator for expected shortfall from Monte Carlo samples. It uses ordered simulated outcomes to estimate the relevant quantile and averages the observations in the tail, with a fractional contribution from the observation…
The document presents ways to validate option pricing and Greek calculations across analytical, finite difference, binomial, and Monte Carlo methods. For models with closed form solutions, it recommends comparing against formulas and worked examples, while…
The post investigates why annualized GARCH(1,1) volatility forecasts from Python's ARCH package matched observed volatility for a more volatile futures return series but appeared far too high for a less volatile series. The author initially assumed that…
The post describes a historical S&P 500 simulation that forms annual portfolios from companies ranked by return on equity: a top group, a bottom group, and a portfolio combining both. Holdings that leave the index are sold and their value redistributed among…
The document presents several proposed ways to set relative objective weights for alpha forecasts and transaction costs in a portfolio optimizer. The setting is monthly standardized factor-model forecasts combined with a nonlinear market-impact model…
The document addresses a survivorship and identifier problem in historical research: finding which exchange-traded funds and real estate investment trusts existed at earlier dates, along with their changing symbols. It points to historical ETF launch,…
The document raises a research question about using Kagi and Renko charting methods on high-frequency foreign-exchange data. The researcher reports applying them across multiple sample lengths and obtaining small positive results, but says cumulative returns…
The document presents a decision problem in which Monte Carlo simulation has produced cost distributions for two alternatives. Their benefits are assumed equal but are not specified, and the decision maker is described as risk averse. Because the simulated…
The document addresses how to revalue an options portfolio in a Monte Carlo VaR simulation when the underlying is simulated with a historical stochastic-volatility model such as GARCH. Its central distinction is that historical volatility of the underlying…
The document presents a simulation of index prices using log returns and a GARCH(1,1) variance recursion. The author selects parameters using the lowest Akaike information criterion and generates repeated paths by drawing innovations from a normal…
The document presents a question about implementing the pathwise derivative method for estimating a call option’s delta under a geometric Brownian motion model. The proposed simulation code evolves prices through multiple time steps and then sums…
The question examines empirical distributions of rolling stock returns calculated over overlapping windows. Because adjacent returns share observations, the series is serially correlated. The author considers thinning the data by sampling every window length…
The document presents a QuantLib setup for calibrating a one-factor Hull–White short-rate model to a EUR overnight-indexed discount curve and a normal-volatility surface for three-month Euribor swaptions. It describes fitting the model’s mean-reversion and…
The document addresses failures in Python workflows that previously fetched foreign-exchange and other historical price data through Yahoo or Google with tools such as pandas datareader and ffn. The accepted answer attributes the Yahoo failure to changes in…
The document asks how to choose a Monte Carlo sample size for estimating a Bernoulli mean to a specified absolute precision. It presents the central limit theorem formula for sample size, using a normal quantile, the outcome variance, and the squared error…
The document outlines a finite-difference approach to pricing a European call by evolving the underlying asset’s probability density under a geometric Brownian motion model. It starts with a forward Kolmogorov equation, discretizes time and the asset-price…